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a. Sketch the graph of the function on the given interval. b. Calculate Ax and the grid points x0, x1, ..., xn. c. Illustrate the left and right Riemann sums. Then determine which Riemann sum underestimates and which sum overestimates the area under the curve. d. Calculate the left and right Riemann sums. 25. f(x) = x +1 on [0, 4]; n = 4

a. Sketch the graph of the function on the given interval. b. Calculate Ax and the grid points x0, x1, ..., xn. c. Illustrate the left and right Riemann sums. Then determine which Riemann sum underestimates and which sum overestimates the area under the curve. d. Calculate the left and right Riemann sums. 25. f(x) = x +1 on [0, 4]; n = 4

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question 25 ( show all work, thank you!)

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25. L a. c. 5 4 2+ 0 YA 5+ 4 3 2 Left Riemann sum underestimates area. b. Ax 2 = y = x + 1 d. 10, 14 2 4 y = x+1 3 Right Riemann sum overestimates area. 4 X 1; xo = 0, x₁ = 1, x₂ = 2, x3 = 3, x4 = 4
Transcribed Image Text:25. L a. c. 5 4 2+ 0 YA 5+ 4 3 2 Left Riemann sum underestimates area. b. Ax 2 = y = x + 1 d. 10, 14 2 4 y = x+1 3 Right Riemann sum overestimates area. 4 X 1; xo = 0, x₁ = 1, x₂ = 2, x3 = 3, x4 = 4
25-32. Left and right Riemann sums Complete the following steps for the given function, interval, and value of n. a. Sketch the graph of the function on the given interval. b. Calculate Ax and the grid points 0, 1, xn. c. Illustrate the left and right Riemann sums. Then determine which Riemann sum underestimates and which sum overestimates the area under the curve. d. Calculate the left and right Riemann sums. 25. f(x) = x +1 on [0, 4]; n = 4 26. f(x) = 9 − x on [3, 8]; n - = 5 27. f(x) = cos x on 0, T 28. T f(x) = sin ㅠ n [0, {] 2 on [0, 3]; n = 6 - T X -1 3 29. f(x) = x² 1 on [2, 4]; n = 4 ; n = 4 30. f(x) = 2x² on [1, 6]; n = 5 31. f(x) = e/2 on [1, 4]; n = 6 32. f(x) = ln 4x on [1, 3]; n = 5 ... 2
Transcribed Image Text:25-32. Left and right Riemann sums Complete the following steps for the given function, interval, and value of n. a. Sketch the graph of the function on the given interval. b. Calculate Ax and the grid points 0, 1, xn. c. Illustrate the left and right Riemann sums. Then determine which Riemann sum underestimates and which sum overestimates the area under the curve. d. Calculate the left and right Riemann sums. 25. f(x) = x +1 on [0, 4]; n = 4 26. f(x) = 9 − x on [3, 8]; n - = 5 27. f(x) = cos x on 0, T 28. T f(x) = sin ㅠ n [0, {] 2 on [0, 3]; n = 6 - T X -1 3 29. f(x) = x² 1 on [2, 4]; n = 4 ; n = 4 30. f(x) = 2x² on [1, 6]; n = 5 31. f(x) = e/2 on [1, 4]; n = 6 32. f(x) = ln 4x on [1, 3]; n = 5 ... 2
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